How to use a Mesh from one project in another?
The Import is for other file formats, you're looking for Link Ctrl-Alt-O or Append Shift-F1 both are accessible from the file menu.

While Append creates an independent copy of your appended objects, Link just references them from the original file. 

If you char consist of more than a single object, you should group Ctrl-G them, this makes it easier to Append or Link.